Fuzzy Scheduling of Logistics Production and Distribution under Uncertain Environments using Particle Swarm Optimization

Transcription

1 XING LIU et al: FUZZY SCHEDULING OF LOGISTICS PRODUCTION AND DISTRIBUTION UNDER Fuzzy Schedulng of Logstcs Producton Dstrbuton under Uncertan Envronments usng Partcle Swarm Otmzaton Xng Lu * Ha Lu School of Management Tanjn Unversty Tanjn Unversty Tanjn Cty Chna School of Busness Zhengzhou Unversty Zhengzhou Unversty Henan Provnce Chna Abstract In ths aer we attemt to ntegrate roducton schedulng dstrbuton routng roblems to mnmze the total cost of the suly chan under uncertan envronments The artcle swarm otmzaton method s used to select the locaton of the dstrbuton center combnng t wth the tabu search algorthm to solve vehcle dstrbuton route roblem Esecally the locaton of each artcle s encoded as a floatng ont number Each artcle conssts of a two row matrx the frst row the locaton of dstrbuton center the second row the ln between dstrbuton center customer The exerment results show that ths scheme can solve roducton-dstrbuton roblems n the global sense effcently In the future convergence seed accuracy based on artcle swarm otmzaton wll be studed to reduce runnng tme of the roosed algorthm ts erformance wll be comared wth other ntellgent comutng technques eywords- Logstcs Producton-dstrbuton; Partcle Swarm Otmzaton; Fuzzy Schedulng Uncertan Envronment I INTRODUCTION The roducton dstrbuton roblems n suly chan s a hotsot of academc research at home abroad the goal of whch s to ntegrate roducton schedulng dstrbuton routng roblem to mnmze the total cost of suly chan[] How to effectvely ntegrate members of the suly chan correctly determne roducton dstrbuton vehcle routng ncreasngly attracts the attenton of the ndustry Otmzaton of enterrse suly chan s helful to mrove oeratonal effcency reduce costs mrove customer satsfacton enhance the comettveness of enterrses[] Imrovng the level of the suly chan must abon the attern that studes each stage searately In the decson-mang of ntegrated suly chan the locaton allocaton roblems vehcle routng roblem are two asects whch attract more attenton n the theory ractce[3]on the bass of the two models other logstc decson model the locaton routng roblem s generated In the decson of faclty oston transortaton cost should be consdered at the same tme For many customers many facltes through the establshment of locaton routng roblem model the otmal number of facltes caacty the otmal transortaton lan route arrangement suly chan cost can be reduced Locaton routng roblem s one of the most concerns under suly chan roductondstrbuton system Locaton routng roblem model s a secal nd of locaton selecton model the basc dea of whch s to consder dstrbuton route otmzaton of vehcles as well as the locaton otmzaton of dstrbuton centres A tycal locaton routng roblem model can be descrbed as follows The number of customers the locaton the dem s nown A comany delvers the goods to the customers from one or more dstrbuton centres there exsts several number of dstrbuton centre locaton for selecton Each customer gets goods only from a dstrbuton centre Hall[3] dvded the vehcle dstrbuton servce nto ndeendent subnets whch s comosed of sngle goods collecton centre multle sngle goods source multle termnals The heurstc algorthm can be used to determne otmal ath for each goods source each termnal of each subnet Ths algorthm can guarantee enough recson s very sutable for large scale ractcal roblems Armacost[4] has carred on the detaled classfcaton research n vew of networ lannng scheme of ar exress mal delvery aren R[5] establshes exress acage dstrbuton model based on mnmzng the total cost A fuzzy evaluaton method of ntegrated logstcs servce networs was roosed by Zhao Zhyan[6] A framewor for transortaton decson mang n an ntegrated suly chan was roosed by Stan TP[7] Otmal roducton allocaton dstrbuton suly chan networs was roosed by Tsas P[8] A mult-agent system to solve the roducton-dstrbuton lannng roblem for a suly chan was roosed by azem A[9] Metaheurstc aroach wth memory evoluton for a multroduct roducton/dstrbuton system desgn roblem was roosed by esn BB[0] An agent-based framewor for buldng decson suort system n suly chan management was roosed by azem A[] Formulatng orderng olces n a suly chan by genetc algorthm was gven by Chan CCH[] Otmzng delvery lead tmenventory lacement n a two-stage roducton-dstrbuton system was wrtten by Barnes-Schuster D[3] Multcrteron genetc otmzaton for due date assgned dstrbuton networ roblems was roosed by Chan FTS[4] Hybrd genetc algorthm for mult-tme erod roducton- DOI 0503/IJSSSTa703 3 ISSN: x onlne rnt

2 XING LIU et al: FUZZY SCHEDULING OF LOGISTICS PRODUCTION AND DISTRIBUTION UNDER dstrbuton lannng was roosed by Gen M[5] Multtem dynamc roducton-dstrbuton lannng n rocess ndustres wth dvergent fnshng stages was roosed by Rz N[6] Dynamc rogrammng decson ath encodng of genetc algorthms for roducton allocaton roblems was roosed by Hua C Y[7] Adotng co-evoluton constrant-satsfacton concet on genetc algorthms to solve suly chan networ desgn roblems was roosed by Yng-Hua C[8] The balanced allocaton of customers to multle dstrbuton centres n the suly chan networ was roosed by Zhou G[9] To sum u study of ostonng roblem of the ath s comaratvely mature both at home abroad but the study of fuzzy customer requrements s relatvely few Locaton-ath roblem n the research s a three layers of the suly chan system wth a sngle factory multle dstrbuton centres customers It s assumed that the factory has no nventory roducts are shed to the dstrbuton centres each dstrbuton centre can serve multle customers each customer can only be suled by a dstrbuton centre The roducton caacty s nfnte transort caacty s lmted Then mathematcal model s set u the man research goal s to mnmze oeraton cost transort cost of the dstrbuton centre The aer s organzed as follows In the next secton model of roducton-dstrbuton s roosed In Secton 3 roducton-dstrbuton fuzzy schedulng based on artcle swarm otmzaton s roosed In Secton 4 the erformance of roosed algorthm s tested At last some conclusons are gven n secton 5 II MODEL OF PRODUCTION-DISTRIBUTION The researched roducton-dstrbuton networ has a fxed locaton of lant multle dstrbuton centres multle fxed oston of clent area Factory has no nventory after the roducts are roduced they are shed drectly to the dstrbuton centre The factory roducton caacty s nfnte t may delver goods to any of the dstrbuton centre (The cost of dstrbuton centre ncludes fxed start-u costs Dstrbuton centres have caacty lmts each dstrbuton centre can suly goods for multle customers The number of avalable vehcles of each dstrbuton centre s nown the vehcle s the same tye The vehcle cannot be used reeatedly can not be transferred to other dstrbuton centre The dem of customer s fuzzy The drected weghted grah G s used to descrbe vehcle routng roblem G ( V A C V { 0 n} vertces set A {( j jv} arc set whch connect C { cj ( j A} each vertces weght Cj matrx dstance between customer to customer j Any vehcle can not surass ts ermtted load each customer s only suled by one vehcle s only served once Each vehcle starts from warehouse returns s { r { } to warehouse at last r one ath of vehcle Each customer s served once each ath starts ends on the same dstrbuton centre the total load caacty s no more than caacty of vehcles The total load of each ath should not exceed caacty of the dstrbuton centre whch s resonsble for the ath The dem of customer s uncertan Producton-dstrbuton model of sngle factorymultle dstrbuton centres-multle customers are as follows c j transortaton cost between j a transortaton cost from factory to dstrbuton centre W the number of dstrbuton centre S start-u cost of dstrbuton centre d j Q dem of customer j caacty of vehcle T start-u cost of vehcles from dstrbuton centre to customer The targeted functon s mn f ( a S y c x Tx j j j I V jv I jj ( The constrants are as follows I x j j J os d jxj Q jj V (3 os djxjy Wy jj V I (4 xj xj 0 jv jv V (5 xj I jj (6 xj S S js S J (7 x {0} j V j V ( (8 y {0} I (9 The formula ( that the sum of dstrbuton centre start-u cost dstrbuton cost of vehcles start-u cost of vehcles s smallest Formula ( ensures that each customer belongs to one route s only accessed once DOI 0503/IJSSSTa703 3 ISSN: x onlne rnt

3 XING LIU et al: FUZZY SCHEDULING OF LOGISTICS PRODUCTION AND DISTRIBUTION UNDER Formula (3 ensures ossblty that meets the vehcle caacty s not less than Formula (4 ensures ossblty that meets the dstrbuton centre caacty s not less than Formula (5 formula (6 ensures that each ath starts ends the same dstrbuton centre Formula (7 ensures the elmnaton of sub-aths Formula (8 whether the vehcle goes through the ath Formula (9 whether the dstrbuton s selected Because formula (3 formula (4 have fuzzy arameters d j ( so some actons should be carred Q Suosng the left caacty of vehcle s after vehcle dstrbutes all customers The left caacty of dstrbuton centre s W after dstrbuton centre serves for all customers comletely Q ( Q Q Q3 ( Q x Q x Q x j j j jj V jj V jj V W ( W W W3 ( Wy x y Wy j jj V x y W y x y j j jj V jj V Q 0 Q os Q Q Q 0 Q ( Q3 Q W 0 W 3 os( W 0 W 0W 3 W3 W 0 W 3 0 Constrants (3 (4 are equvalent to the followng nequaton os( Q 0 os( W 0 I III PRODUCTION-DISTRIBUTION FUZZY SCHEDULING The ntal value s roduced by means of fuzzy c-means algorthm The n number of elements s searated nto c number of clusterng The weghted square sum between each data ont each clusterng centre s c n m J ( x v FCM j j j (0 xj the vector feature of the j-th customer v the -th clusterng centre j membersh of the j-th customer to the -th clusterng centre m convergence arameter whch controls convergence seed The membersh degree s calculated by means of harmoncmean The rocess of calculatng ntal soluton s as follows Ste Set the mnmal error value of dstance between ntal clusterng centre the new centre Ste Determne the ntal number of clusterng whch s determned by the total customer dem caacty of each vehcle Ste3 After determnng c number of clusterng c number of average value s taen as ntal centre of the clusterng Ste4 Calculate membersh values between the current customers clusterng centres Chec the membersh value of each customer to select the cluster wth the hghest membersh value ths customer s assgned to ths cluster At ths tme t s requred to determne whether t conforms to constrant of the vehcle caacty If t meets the constrant the customer dem accumulates to the vehcle caacty n ths cluster turn to the next customer untl all of the customers belong to ther corresondng clusters Ste5 The vehcles of the full caacty are not consdered then determne whether there exsts clusterng centres If there exsts clusterng centres return to ste 4 Otherwse the udate stos The contnuous dstrbuton centre locaton model s encoded locaton of each artcle s encoded wth floatng ont number Each artcle conssts of a two row of matrx the frst row the locaton of dstrbuton centre the second row dstrbuton between dstrbuton centre customer The ntal locaton of dstrbuton centre s m number of floatng ont number ( x whch s y [ x y x y xm ym] m xc0 x xc yc 0 y yc ( xc0 yc0 the coordnates at the startng ont ( xc yc the coordnates at the end ont z j z The dstrbuton ath s reresented by j that the ath between dstrbuton centre customer j s selected The artcle seed conssts of a two row of matrx the frst row of whch s m number of floatng v [ v ont number v vm ] The number of artcles s n the dmenson of searchng sace s D X ( x x xd P ( locaton of the -th artcle D or the hstorcal oston In the swarm DOI 0503/IJSSSTa ISSN: x onlne rnt

4 XING LIU et al: FUZZY SCHEDULING OF LOGISTICS PRODUCTION AND DISTRIBUTION UNDER g the hstorcal locaton of all artcles s mared as V ( v v vd the seed of artcle Partcle locaton seed are adjusted accordng to resectvely v wv c r ( x x d d x d c r ( v d d gd d x d d ( ( c c are constant w s nerta weght r x d r [0] are rom numbers belongng to the d-th dmenson comonent of locaton vector of artcle v n the -th teraton d the d-th dmenson comonent of seed vector of artcle n the - th teraton d the d-th dmenson comonent of ndvdual oston of artcle gd g the d-th dmenson comonent of global oston of artcle The locaton of dstrbuton centre can be calculated by artcle swarm otmzaton Ste Intalze the seed locaton of the artcle Ste Calculate ftness value of each artcle n the swarm Hstorcal otmal value hstorcal otmal locaton corresondng to ths artcle are obtaned The ndvdual wth the ftness value n the swarm s taen as the global otmal value f ( z ( a S y ftness f ( z I Ste3 Udate the seed locaton of all artcles accordng to ( ( Ste4 Calculate ftness value for each artcle The ftness values are comared wth hstorcal otmal value of the ndvdual If the ftness value s better than hstorcal otmal value of the ndvdual the new locaton s taen as the new hstorcal otmal value of ths artcle Comare the ndvdual otmal value wth the global otmal value to determne the new global otmal value Ste5 Determne whether t meets the stong condton outut result Otherwse turn to ste 3 f ( z cj xj Txj V jv I jj s a tycal vehcle ath roblem whch can be solved by tabu search algorthm Produce L number of natural number arrangement whch are not reeated The natural number encodng s based on vehcle ath order Accordng to the constrant condton of vehcle routng roblem the customers n the ndvdual can be assgned nto each dstrbuton ath n turn If a customer ont s selected to erform an nsert oeraton t cannot be selected n the next few generatons In the same way all customers can be ncororated nto the ath It meets the constrant that a dem ont can be accessed once For dstrbuton routng scheme corresondng to a quas selected customer ont the followng ways are used to determne ther advantages dsadvantages One s to calculate the value of the objectve functon namely the dstance travelled by dstrbuton centre for all customers The other way s to determne whether t satsfes the constrants of the roblem Neghborhood search method s as follows Some customer n the soluton s s moved from current locaton to another locaton of s to generate the new soluton The customer locaton j n the soluton s are swaed to generate the new soluton The two customers j on the same ath n the soluton s are mared as j resectvely The customer at oston s swaed wth j customer nodes between j accessed accordng to the reverse order The acceted soluton after each teraton s tae as taboo object whch s ut nto the taboo table After a fxed number of teraton the algorthm stos IV NUMERICAL EXAMPLES There are four number of dstrbuton centres one enterrse twenty number of customers The coordnates range of customers are generated romly from (0 0 to (00 00 The dem s generated romly from 0 to 00 The dstance s Eucldean dstance cj 06 yuan / m 095 For the artcle swarm otmzaton w 6 c 7 c 7 the maxmum teraton number s 00 For the tabu search algorthm tabu length s 8 50 number of adjacent areas of current soluton are searched n each teraton Fxed cost of establshng the dstrbuton centre s shown n table I The maxmum caacty of each dstrbuton centre s shown n table II The locaton dem of each customer s shown n table III the locaton of each dstrbuton centre s shown n table IV TABLE I FIXED COST OF ESTABLISHING THE DISTRIBUTION CENTRE dstrbuton centre 3 4 fxed cost TABLE II MAXIMUM CAPACITY OF EACH DISTRIBUTION CENTRE dstrbuton centre 3 4 caacty(ton DOI 0503/IJSSSTa ISSN: x onlne rnt

5 XING LIU et al: FUZZY SCHEDULING OF LOGISTICS PRODUCTION AND DISTRIBUTION UNDER TABLE III A THE LOCATION AND DEMAND OF EACH CUSTOMER customer number coordnates(m (306 (8 fuzzy dem(t ( ( customer number 5 6 coordnates(m (408 (406 fuzzy dem(t (99498 ( customer number 9 0 coordnates(m (7056 (5650 fuzzy dem(t (77886 ( customer number 3 4 coordnates(m (688 (5660 fuzzy dem(t ( ( customer number 7 8 coordnates(m (938 (4480 fuzzy dem(t (79886 ( TABLE IV B THE LOCATION AND DEMAND OF EACH CUSTOMER customer number 3 4 coordnates(m (94 (66 fuzzy dem(t ( (78790 customer number 7 8 coordnates(m (7746 (769 fuzzy dem(t (78086 ( customer number coordnates(m (5069 (446 fuzzy dem(t ( (57606 customer number 5 6 coordnates(m (896 (4049 fuzzy dem(t ( (88995 customer number 9 0 coordnates(m (070 (659 fuzzy dem(t ( (68775 TABLE V THE LOCATION OF EACH DISTRIBUTION CENTRE dstrbuton 3 4 number horzon axs vertcal axs The selected dstrbuton centres are centre centre 3 One dstrbuton ath s the other dstrbuton ath s V CONCLUSION Producton-dstrbuton fuzzy schedulng under uncertan envronment n the logstcs ndustry s nvestgated There s one factory multle dstrbuton centres multle customers n the suly chan The artcle swarm otmzaton s used to select the locaton of dstrbuton centre tabu search algorthm s used to solve vehcle dstrbuton route roblem The exerment results show that ths scheme can solve roducton-dstrbuton roblem n the global sense effcently But the roosed algorthm has some dsadvantages Tradtonal artcle swarm otmzaton s easy to fall nto local otmum so that ts convergence seed accuracy can be further mroved Fuzzy-c means algorthm s nfluenced greatly by ntalzaton whch can be otmzed by ntellgent comutng such as genetc algorthm artcle swarm otmzaton so on Besdes genetc algorthm other ntellgent comutng can be used to select the locaton of dstrbuton centre the result of whch can be comared wth the result of roosed scheme In the future convergence seed accuracy based on artcle swarm otmzaton wll be studed REFERENCES [] Mar W H Morton E o Embeddng economes of scale concets for hub networ desgn Journal of Transort Geograhy vol [] Bllonnet A Elloum S Grouz-Djerb L Desgnng radomoble accessnetwors based on synchronous dgtal herarchy rngs Comuters oeratons Research vol [3] Hall R W Drect versus termnal freght routng on a networ wth concavecosts Transortaton Research Part vol [4] Zhao Zhyan etc A Fuzzy Evaluaton Method of Integrated Logstcs Servce Networs The 6 th Internatonal Conference on Management ConferenceLondon [5] Stan TP Goldsby TF A framewor for transortaton decson mang n an ntegrated suly chan Log Inform Manag vol [6] Tsas P Paageorgou LG Otmal roducton allocaton dstrbuton suly chan networs vol [7] azem A Fazel Zar MH Moattar Hussen SM A mult-agent system to solve the roducton-dstrbuton lannng roblem for a suly chan: A Genetc algorthm aroach Manufact Technol vol [8] esn BB Uster H Meta-heurstc aroaches wth memory evoluton for a mult-roduct roducton/dstrbuton system desgn roblem Eur J Oer Res [9] azem A Fazel ZMH An agent-based framewor for buldng decson suort system n suly chan management J Al Sc [0] Chan CCH Cheng CB Huang SW Formulatng orderng olces n a suly chan by genetc algorthm Int J Model Smulat [] Barnes-Schuster D Basso Y Anund R Otmzng delvery lead tme-nventory lacement n a two-stage roducton-dstrbuton system Eur J Oer Res vol [] Chan FTS Chung SH Multcrteron genetc otmzaton for due date assgned dstrbuton networ roblems Decs Suort Syst vol [3] Gen M Syarf A Hybrd genetc algorthm for mult-tme erod roducton-dstrbuton lannng Comut Ind Eng vol [4] Rz N Martel A D Amours S Mult-tem dynamc roductondstrbuton lannng n rocess ndustres wth dvergent fnshng stages Comut Oer Res vol [5] Hua C Y Hou Y C Dynamc rogrammng decson ath encodng of genetc algorthms for roducton allocaton roblems Comuters & Industral Engneerng vol [6] Yng-Hua C Adotng co-evoluton constrant-satsfacton concet on genetc algorthms to solve suly chan networ desgn roblems Exert Systems wth Alcatons vol [7] Zhou G Mn H Gen M The balanced allocaton of customers to multle dstrbuton centres n the suly chan networ: a genetc algorthm aroach Comuters & Industral Engneerng vol DOI 0503/IJSSSTa ISSN: x onlne rnt